Question: Solve for $x$ and $y$ using elimination. ${-4x+5y = 8}$ ${x+4y = 19}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${-4x+5y = 8}$ $4x+16y = 76$ Add the top and bottom equations together. $21y = 84$ $\dfrac{21y}{{21}} = \dfrac{84}{{21}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-4x+5y = 8}\thinspace$ to find $x$ ${-4x + 5}{(4)}{= 8}$ $-4x+20 = 8$ $-4x+20{-20} = 8{-20}$ $-4x = -12$ $\dfrac{-4x}{{-4}} = \dfrac{-12}{{-4}}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {x+4y = 19}\thinspace$ and get the same answer for $x$ : ${x + 4}{(4)}{= 19}$ ${x = 3}$